Fire mage does more damage, has better survivability, better single target DPS and better AoE but is a lot harder to play. You need to time combustions to line up with crits and let ignites roll until you get good crits and then finally once everything lines up slap a combustion on there and enjoy absolutely absurd numbers.

If you wanna do similar single target DPS by binding the whole keyboard to one button and rolling your fase from the left to the right (some studies have said rolling from right to left is also viable but more theorycrafting needs to be done) then go with arcane.

The only fight an arcane mage is legitimately better on is Spine of Deathwing hc where they can burst down the tendon like mad, but it's so much easier to play you will probably see better results facerolling arcane until you properly learn fire.